3 ms·
I also do not understand the intuition behind the assumption. To tie two knots together, you have to make a cut in both of them, and you have two ways to tie th
by Someone 1y ago
I also do not understand the intuition behind the assumption. To tie two knots together, you have to make a cut in both of them, and you have two ways to tie them together again. Doesn’t that introduce some opportunity to get rid of some complexity of the knots?
- masterjack 1y agoRemarkably there’s really just one way to tie them together, you can always manipulate the knot to move between the different variants
- aleph_minus_one 1y ago> Remarkably there’s really just one way to tie them together I would rather assume (but knot theorists shall correct me if I'm wrong) that there exist two ways of tying them together: Cut knots K, L at some point; denote the loose ends by K1, K2, L1, L2. - Option 1: connect K1 <-> L1, K2 <-> L2 - Option 2: connect K1 <-> L2, K2 <-> L1
- cottonseed 1y agoThose are the same. To see that, just flip over L before performing the connect sum.
- cluckindan 1y agoIf they are the same, the mirrored double-chiral knot from the article would have identical properties even if one of the knots wasn’t mirrored.